---
tag: CN7HK9K1B6
kind: concept
name: Neighborhood semantics
aliases: [neighbourhood-semantics, scott-montague-semantics]
sources:
  - wikipedia: en:5809298@r1339444889
    locator: Neighborhood semantics
    note: adopted
    mention: wikipedia://en/5809298
    sections: [Summary]
same_as:
  wikidata: Q6988052
  wikipedia: Neighborhood semantics
inventory: [K2P1X1AQVB]
---

## Summary

**Neighborhood semantics**, also known as **Scott–Montague semantics**, is a formal semantics for modal logics. It is a generalization, developed independently by Dana Scott and Richard Montague, of the more widely known relational semantics for modal logic. Whereas a relational frame $\langle W,R\rangle$ consists of a set *W* of worlds (or states) and an accessibility relation *R* intended to indicate which worlds are alternatives to (or, accessible from) others, a **neighborhood frame** $\langle W,N\rangle$ still has a set *W* of worlds, but has instead of an accessibility relation a *neighborhood function*